# Function Definitions

get_conus_spatial <- function(data, var, proj = 5070, abb = FALSE) {
    # Filter CONUS from a spatial US dataset and modify its projection.
    #
    # Args:
    #   data: Spatial US dataset to filter.
    #   var: Column of "data" that contains states' information.
    #   proj: EPSG code to project dataset to, defaults to EPSG:5070.
    #   abb: If TRUE, then states in "var" are denoted with abbreviations;
    #        If FALSE, then states in "var" are denoted by their full names.
    #
    # Returns:
    #   A spatial CONUS dataset projected to given EPSG code.
    if (abb) {
        conus <- filter(data,
            !(get(var)) %in% c("AK", "HI", "PR", "GU"))
    } else {
        conus <- filter(data,
            !(get(var)) %in% c("Alaska", "Hawaii", "Puerto Rico", "Guam"))
    }

    conus <- sf::st_transform(conus, proj)
    return(conus)
}

generate_tiles <- function(data, tile_type = TRUE) {
    # Generate tiled spatial data from four tessellation/coverage options.
    #
    # Args:
    #   data: Spatial dataset to tesselate
    #   tile_type: "square" - square coverage with "n = 70"
    #              "hexagonal" - hexagonal coverage with "n = 70"
    #              "voroni" - voroni tesselation
    #              "triangulate" - Delaunay triangulation
    #              none of the above - unmodified data
    #
    # Returns:
    #   A spatial, tiled dataset from a given dataset and
    #   tessellation/coverage type or unmodified data.

    if (tile_type == "square") {
        tiled_data <- sf::st_make_grid(data, n = 70)
    } else if (tile_type == "hexagonal") {
        tiled_data <- sf::st_make_grid(data, n = 70, square = FALSE)
    } else if (tile_type == "voroni") {
        tiled_data <- sf::st_centroid(data) %>%
            sf::st_combine() %>%
            sf::st_voronoi() %>%
            sf::st_cast()
    } else if (tile_type == "triangulate") {
        tiled_data <- sf::st_centroid(data) %>%
            sf::st_combine() %>%
            sf::st_triangulate() %>%
            sf::st_cast()
    } else {
        return(data)
    }

    tiled_data <- sf::st_as_sf(tiled_data) %>%
        mutate(id = 1:n())

    return(tiled_data)
}

plot_map <- function(data, title = "", include_features = TRUE) {
    # Plot spatial data using ggplot() + geom_sf().
    #
    # Args:
    #   data: Spatial dataset to plot.
    #   title: Title shown on plot.
    #   include_features: If TRUE, include caption of features collected.
    #
    # Returns:
    #   A plotted ggplot() map with, a white background,
    #   navy border, size = 0.2, features collected, and given title.

    ggplot() +
        geom_sf(
            data = data,
            fill = "white",
            colour = "navy",
            size = 0.2
        ) +
        theme_void() +
        labs(
            title = title,
            caption = if (include_features) {
                paste(nrow(data), " features collected")
            } else {
                ""
            }
        )
}

Function Definitions

For explicit function code, click the above “Code” button.

get_conus_spatial()

Filter CONUS from a spatial US dataset and modify its projection.

Args:
    data: Spatial US dataset to filter.
    var: Column of "data" that contains states' information.
    proj: EPSG code to project dataset to, defaults to EPSG:5070.
    abb: If TRUE, then states in "var" are denoted with abbreviations;
         If FALSE, then states in "var" are denoted by their full names.

Returns:
    A spatial CONUS dataset projected to given EPSG code.

generate_tiles()

Generate tiled spatial data from four tessellation/coverage options.

Args:
  data: Spatial dataset to tessellate
  tile_type: "square" - square coverage with "n = 70"
             "hexagonal" - hexagonal coverage with "n = 70"
             "voroni" - voroni tesselation
             "triangulate" - Delaunay triangulation
             none of the above - unmodified data

Returns:
  A spatial, tiled dataset from a given dataset and
  tessellation/coverage type or unmodified data.

plot_map()

Plot spatial data using ggplot() + geom_sf().

Args:
  data: Spatial dataset to plot.
  title: Title shown on plot.
  include_features: If TRUE, include caption of features collected.

Returns:
  A plotted ggplot() map with, a white background,
  navy border, size = 0.2, features collected, and given title.
# Step 1.1
conus_counties <- get_conus_spatial(USAboundaries::us_counties(), "state_name")

# Step 1.2/1.3
conus_square <- generate_tiles(conus_counties, "square")
conus_hexagonal <- generate_tiles(conus_counties, "hexagonal")
conus_voroni <- generate_tiles(conus_counties, "voroni")
conus_triangulate <- generate_tiles(conus_counties, "triangulate")

# Testing before Step 1.4/1.5

Checking Plots

Square Coverage

Hexagonal Coverage

Voroni Tessellation

Delaunay Triangulation

Tidying Tessellations

conus_border <- st_union(conus_counties)
conus_simple <- conus_border %>%
    rmapshaper::ms_simplify(keep = 0.05)

One thing to notice about the data that we are going to perform analysis on, in particular the tessellated spatial datasets, is that we have a lot of surrounding excess data. The goal here with tidying these datasets is to create a suitable dataset for performing analysis on, and in this case, that means specifically CONUS representative data. The first thing we will do is to create a simplified border of CONUS:

ggplot() +
    geom_sf(data = conus_border) +
    theme_void() +
    labs(subtitle = paste(
                        "Unioned CONUS Points: ",
                        mapview::npts(conus_border)
                    )
        )

ggplot() +
    geom_sf(data = conus_simple) +
    theme_void() +
    labs(subtitle = paste(
                        "Simplified CONUS Points: ",
                        mapview::npts(conus_simple)
                    )
        )

By simplifying we were able to remove 3068 points, while still keeping roughly the same shape that we want. While it may seem that we do not want to lose data, for the analysis that we will be doing, a great amount of detail isn’t necessary. Here, we want to visualize the overlap of our simplified CONUS border over our tessellations, so that we can see exactly what are trying to get rid of Note that, while the overlapping CONUS border looks like it is a MULTILINESTRING, it’s really a geom_sf() with fill = NA. Now, notice the border excludes most of the excess data surrounding the tessellated spatial datasets that we do not need:

# Overlapping Plot with CONUS map to cut edges
ggplot() +
    geom_sf(data = conus_voroni, fill = NA) +
    geom_sf(
        data = conus_simple,
        color = "green",
        fill = NA) +
        theme_void() +
        labs(subtitle = paste(
                            "Simplified CONUS Points: ",
                            mapview::npts(conus_simple),
                            "\n",
                            "Voroni Tessellation Points: ",
                            mapview::npts(conus_voroni)
                       )
            )

# Overlapping Plot with CONUS map to cut edges
ggplot() +
    geom_sf(data = conus_triangulate, fill = NA) +
    geom_sf(
        data = conus_simple,
        color = "green",
        fill = NA) +
        theme_void() +
        labs(subtitle = paste(
                            "Simplified CONUS Points: ",
                            mapview::npts(conus_simple),
                            "\n",
                            "Delaunay Triangulation Points: ",
                            mapview::npts(conus_triangulate)
                       )
            )

Using sf::st_intersection(), we can get rid of the excess data. Using this function, we have the following spatial datasets:

# Plot tidied voroni
conus_voroni_tidy <- st_intersection(conus_voroni, conus_simple)
plot_map(
    conus_voroni_tidy,
    title = "Tidied Voroni Tessellation",
    include_features = FALSE
)

# Plot tidied triangulation
conus_triangulate_tidy <- st_intersection(conus_triangulate, conus_simple)
plot_map(
    conus_triangulate_tidy,
    title = "Tidied Delaunay Triangulation",
    include_features = FALSE
)

So, this gives us each spatial dataset that we will be using:

Spatial Datasets

Original

Square Coverage

Hexagonal Coverage

Voroni Tessellation

Delaunay Triangulation